three dimensional figures, objects solid unit 6 math vocabulary three dimensional figures, objects solid

What is volume?

The space inside a 3D figure.

What makes a shape 3D?

It must have height.

Volume vs Area

Volume is for 3D shapes

Area is for 2D shapes

Exponents for volume vs area

Volume → exponent of 3 (cubed)

Area → exponent of 2 (squared)

General volume formula

Volume = B × H

B = area of the base

H = height

Rectangular prism formula

V = length × width × height

Triangular prism formula

V = 1/2 × base × height × height

(one height for triangle, one for prism)

Triangular prism has two height

Cube formula

V = side × side × side Or

(s³) or

S x s x h

Cylinder formula

V = π × r² × h

Cone formula

V = 1/3 × π × r² × h

What do all pointy shapes have in common with there volume formula ?

They start with 1/3 in the formula

Square pyramid formula

V = 1/3 × side × side × height

Rectangular pyramid formula

V = 1/3 × length × width × height

Sphere formula

V = 4/3 × π × r³

Hemisphere formula

Take sphere formula and divide by 2

What is radius?

Half of the circle

What is diameter?

The whole distance across the circle

What must you know before solving density and mass problems?

You must know volume.

What is mass?

The amount of matter in an object.

What is density?

How tightly matter is packed in a substance.

Mass formula

Mass = Density × Volume

Density formula

Density = Mass ÷ Volume

What does g/cm³ mean

Grams per cubic centimeter

It is a unit of density